Metamath Proof Explorer


Theorem exp45

Description: An exportation inference. (Contributed by NM, 26-Apr-1994)

Ref Expression
Hypothesis exp45.1 ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒𝜃 ) ) ) → 𝜏 )
Assertion exp45 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )

Proof

Step Hyp Ref Expression
1 exp45.1 ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒𝜃 ) ) ) → 𝜏 )
2 1 exp32 ( 𝜑 → ( 𝜓 → ( ( 𝜒𝜃 ) → 𝜏 ) ) )
3 2 exp4a ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )